Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Composition of Inverses

Consider the function \(f\) defined for all real numbers:
\[f(x)= \begin{cases}
x+a & \text{ if } x<8 \\
3x-1 & \text{ if } x\geq 8.
\end{cases} \]
If it has an inverse function that is also defined for all real numbers, what is the value of \[(f^{-1}\circ f^{-1})(65)?\]